Friday, April 30, 2010

After defining the concept of character survivability (and providing a tool for calculating it), I think it's time to explore its applications. Today I'll study the S (survivability) values of three different characters, representative of each party role: a defender, a controller, and a striker/leader (since both roles share similar amounts of HP and defenses). I'll compare their progression across the 30 levels of the game, examining survivability for individual defenses as well as overall survivability.

I'd like to find out whether the relative resilience of each role remains stable throughout tiers, or it presents large variability due to scaling differences. Also, I want to analyze absolute survivability values, and their implications on combat length - having defined the metric as the number of turns until a PC is killed by a monster of the same level, these numbers should provide a very rough estimation (i.e. before accounting for healing and stunned monsters) of the maximum duration of an encounter of the PC's level. The minimum duration, of course, would be dependant on the party DPR... but that is a story for another day. Let's proceed with the experiment.

The sample characters.

One requirement of this study is to have a set of sample characters whose survivability values could be representative of their role. Since defensive statistics can vary considerably, even for a given class/race combination, depending on the choice of feats and items, this is no trivial task. In order to keep complexity at a manageable level, we will make the following assumptions:

- Each character starts at level 1 with average defensive stats for their role.

- It is assumed that the character takes the feats and ability increases necesary to keep AC stable as they level up. Other than that, no survivability-boosting feats or items are considered. Any actual PC who invests in survivability should show values above these, particularly at higher levels.

- The leader role and striker role are considered equivalent from a survivability point of view. From now on, when I mention the "striker" character, it applies to either role.

It is impossible to keep normalized AC completely stable across levels, but the deviations are usually minor. I have opted for using constant values because these variations depend more on the choice of heavy or light armor than on actual role, and are usually compensated over a character's whole career.

Non-AC Defenses

For Fortitude, Reflex and Will, I decided to make a small abstraction, and consider only "good defenses" and "bad defenses", regardless of how they were allocated. I have also considered them role-independent, so all three characters show the same progression. The progression itself was taken from the values generated for the character PC2 in this article. PC 2 is a character with 2 "good" defenses, and we defined it as follows:

"The second sample character, PC2, has well-balanced NADs, with only one bad defense and a starting ability array of 16, 16, 12, 12 (pre-racials). This character would have racial bonuses to both primary and secondary abilities, and a +2 class bonus to the best defense, for starting NAD scores of 16, 14, and 11 (from best to worst defense). This character could be a Whirling Barbarian or a Chaos Sorcerer, among others."

Only the best and worst defense for PC2 have been used (as "good" and "bad" values, respectively), discarding the middle one. For the overall survivability of our three characters, we will make two calculations: one assuming they have two good defenses, and another assuming they have two bad ones. This introduces a small error, since the best defense of a character tends to be slightly higher if it is the only good one but, again, the gain in simplicity outweights the loss in accuracy.

The results

This graph shows the Survivability progression for attacks against AC:

This is where the greatest differences among roles show up. As we can see, the values for defenders roughly double those for controllers. As for strikers they start out very close to controllers, but slowly overtake them as the difference in HP grows more important over levels, capping at around 20% more at level 30.

Also interesting is the fact that absolute survivability values experiment considerable growth, more than doubling between level 1 and 30. This is in spite of the fact that the monster hit rates remain constant - the relation between PC hit points and monster damage becoming more and more favorable to the PCs.

The following figures show S for "good" and "bad" non-AC defenses:

Since non-AC defenses don't vary depending on role, the relative S values here are much closer, reflecting only the HP diferences of each role. Keep in mind that normalized defenses are actually diminishing as the character levels up (specially for the bad defense), but overall survivability still grows because of the unbalance between PC hit points and monster damage. Nevertheless, this growth is not as pronounced as AC survivability, and values at maximum level end up slightly below double those of level 1. Also of note is the fact that defenders are much more vulnerable against NAD attacks than against AC attacks, whereas strikers and controllers find their AC roughly equivalent to their good NADs. Bad defenses, as expected, are terrible for all characters, though it is interesting to see that their S values remain more or less constant, rather than getting worse as the characters level up.

Finally, we can average the values shown above to figure out the overall survivability of each character. As we can see, the differences between the builds with 2 good NADs and 1 good NAD aren't actually very significant, with regards to overall survivability. This can be explained by the fact that having an additional good NAD will only come up on 1/6 of attacks. Nevertheless, these figures hide other negative consequences of bad NADs, such as the higher variability among encounters (increasing the chance that enemies auto-hit you), as well as a huge vulnerability to attacks that inflict status effects (as opposed to raw damage, which is what S measures).

It is also possible that the coefficients used to average overall S (1/3 for AC, 1/6 for other defenses) need to be adjusted at paragon and epic tiers, since there seems to be a greater amount of NAD attacks for monsters of these tiers. However, since I lack solid data on that matter, I'll stick with my original approximation until I find some statistical analysis of the different monster manuals.

Conclusions

The relative resilience of the different roles is more or less as could be expected, with defenders being twice as tough, and controllers falling slightly behind strikers. However, we must remember that these are just baseline values - for real builds, non-defenders tend to have a lot more potential for improvement, specially for AC, so the gap with a defender should be much narrower if a player decides to invest in resilience. On the other hand, the temporary hit point gaining of some defenders are more rare among other roles, and would grant them an edge. The same could be said of damage resistance. I'll try to talk about this in a future post.

As for the implications of survivability on encounter length, we find that a group of same-level monsters will need more than twice the amount of time to kill a level 30 party, compared to one of level 1. That is, if the level 1 PCs can expect the monsters to defeat them after 6 or 7 turns of combat, the level 30 ones would live for more than a dozen turns. That is, of course, assuming that the PCs just stand around doing nothing - in an actual encounter, PCs will get healed, and monsters will gradually die, so the real time before the defeat should be significantly higher.

We can also apply these results to analyze the effect of focused monster attacks on a single character. Using the standard of 5 characters per party, the monster group would be able to knock out a level 1 non-defender in a single round, whereas the defender would survive for another round. At epic tier, the non-defender would endure 2 whole rounds of punishment, and the defender more than 3.

Monday, April 19, 2010

Most of the current game theory for D&D 4E is focused on measuring and comparing each character's offensive prowess. There are several reasons for this: damage-dealing is the most common role in adventuring parties, and quantifying the result of an attack is relatively straightforward. Also, players just love to destroy monsters (and peers) with absurdly high damage numbers. But even the most well-oiled killing machine needs some degree of defensive capabilities, lest his enemies knock him down in a single turn (as certain players in my group can attest).

But how do you measure survivability? It's trivial to come up with damage as the universal unit for comparing attacks, but which one should be used for toughness? It should factor in Hit Points, Armor Class, and the other three defenses - and also mechanics such as resistance or temporary hit points. After considering the issue for a while, I think I have come up with a good solution: we can (and should) calculate the number of turns that a character can endure monster attacks before becoming unconscious. The basic formula would have the following form:

Survivability = Character HP / Enemy's average attack damage

or, abbreviated:

S = HP / monster DPRS (survivability), as defined above, provides a good estimate of the effort required to bring a character down. Players can use it to have a better knowledge of the resilience of each member of a party, or of different builds for a certain character. As an example, it would be a useful tool to determine whether it is better to invest in higher defenses, hit points, or resistance, at any given time.

One disclaimer, though: there are aspects of a character's resilience that aren't covered by this stat. Specifically, it doesn't describe how well a character staves off negative conditions - for that, you need to resort to AC and the other defenses. For this reason, when you see two characters with the same survivability, both will be able to endure the same number of attacks, but the one with higher defenses (and, conversely, lower HP and resistance) will suffer less from hindering effects.

This Survivability formula implicitly assumes that the enemy attacks are targeting a specific defense (since we wouldn't be able to calculate average damage otherwise). For this reason, a character will actually have four different S values: S(AC), S(For), S(Ref) and S(Wil). We can define overall survivability (or just S) as the weighted sum of all defense-specific S values:

S= 1/2* S(AC) + 1/6* S(For) + 1/6*S(Ref) + 1/6*S(Wil)

Note that Fortitude, Reflex and Will are all worth the same, and AC counts as much as the three together. This roughly reflects the frequency with which monsters tend to attack each defense - it may not be exact, but I think it's close enough.

The mandatory math section

If you want to play a bit with the idea of survivability, find out actual values for your PCs, and see how long a bunch of theoretical Skirmishers of your level would need to kill you, the quickest way is to go to my online Survivability calculator and start introducing stats. On the other hand, if you are curious as to how it works, this is how the formulas break down:

The above formulas are accurate except for extremey high values of resistance. In particular, any resistance greater than the monster bonus to damage will not be as effective as the formulas show, because monsters never do negative damage. This way, a creature which deals 1d10-5 damage after substracting resist would not average 0.5 damage (5.5 average from the die, -5), but a few points more than that. This is a rare occurrence because such high resistances are very hard to get outside of short term powers, but you should be aware that it exists.

Future refinements

In addition to adding critical damage, there are a few improvements that could be added to this model (and to the calculator!). The most urgent would be the calculation of S values for characters (usually defenders) that can gain temporary hit points each time they attack. This is slightly more complicated than the basic case, as it depends on the character's own hit rate, and varies depending on the number of attacking enemies. I'll write about that in the following days, and add it to the code as soon as I can.

Apart from that, I'd like to hear some reader feedback. Can you think of ways to improve this model? Let me know!

Friday, April 16, 2010

Update: A more advanced version of the calculator has been released, featuring compatibility with temporary hit points, regeneration, and defense-boosting attacks. You can find it here.

Here is a tool I've been working on lately. Just type in your PC's stats, and it will calculate the time a skirmisher monster of a given level needs to bring you to 0 HP. It's still a bit rough, as it doesn't take into account crits, temporary HP, or high resistance values. Still, I have found it both useful and entertaining.Expect discussion of the underlying math, the approximations involved, and the (brand new!) concept of character survivability in an upcoming post. Until then... enjoy!

Note: I have tested this with Firefox and Chrome. Unfortunately, it doesn't seem to work yet with Explorer, but I'm working on it.

Thursday, April 15, 2010

I have updated my index of weapon-related feats with the new material from Martial Power 2 and Player Handbook 3. They are classified by weapon category and ordered by tier, with different sections for generic feats and for those that require specific races or classes. I also list the source books, for those who lack DDI subscriptions, though this will be a lot more useful if you can see the Compendium tootips.

Thursday, April 8, 2010

This month, in Dragon magazine, Warlocks get another amazing article. No, really. Again. It definitely looks like someone at Wizards is badly in love with Warlocks. Of the tiefling variety. And is Lead Designer of the game, and thus allowed to do silly things, like using Charisma for Infernal Pact powers, and get away with it.

It's cool to be with the charismatic boys!

Yes, intrepid reader! The days where Star Pact Warlocks sat lonely as the one class build with weird stats have come to an end, as the Infernal Pact joins the club. Of course, the devil is in the details, because this time the designers have not forgotten to provide an alternate at-will for charismatic characters. This power, called Gift to Avernus, is a very nice clone of Eldritch Blast which features a shiny new mechanic from hell: taking damage to reroll an attack.

Let us take a close look at this mechanic, because it is shared by all the powers introduced in this article. The base idea is simple: when you miss, take damage and make a new attack roll. The question that most sensible Warlocks should be making by now is not 'why would I use a spell that hurts me', but 'how much damage, did you say?'. We're talking about practical people, after all.

The cost is equal to your level in HP. This is a real bargain at the very first level, but don't be fooled by that anomaly - it soon stabilizes into something closer to 10-15% of your total health. Depending on your tier, this may or may not be more than a round's worth of monster damage. That's quite a lot! This makes focusing on these powers a risky proposition, unless you are just not being attacked, or you somehow have a bunch of extra HP lying around. Enter Dark One's Blessing.

Isn't it an amazing coincidence that the infernal warlock's pact boon grans them exactly the temporary hit points they'd need to pay for a reroll with these powers? The existence of this feature drastically changes our evaluation of these powers, from something dangerous and probably not worthwhile, to a good outlet for the absurd amounts of THP you naturally gained, and usually wasted. If you ever feel that you won't have enough temporaries to consistently support this, just add Bloodied Boon...

With that out of the way, what do the powers look like? The at-will, in my opinion, is a very good proposition, leaving the reroll as an option, and granting full effect if you hit the second time. As for the encounter powers (one for each level), they are a bit trickier, since they actually force you to take the damage, and then only repeat the attack against a different enemy, and with reduced damage. Nevertheless, I think they are well worth the pain.

Reliability with damaging attacks is important for a striker, and most of these powers deal more than enough damage by themselves (in addition to granting extra chances for your curse damage). But it is probably even better when you are inflicting significant control effects. And we are also getting a good score in that regard! You have immobilizations, automatic self-attacks (triggering defender marks), enemies trapped in zones, sliding enemies in an area... most of them both interesting and strong. My personal favourite is a level 7 power called Pain to Pleasure, which heals you if you hit, then hurts you on a miss only to heal you again, if you hit the second time. Wicked!

The power selection is barely enough to support a Charisma-based infernal warlock throughout his career, provided he takes generic or off-pact dailies (since they are not included). This doesn't allow for much variety, but since every power presented is quite decent, if not actively good, you should be able to pull it off. Also, many of the new options are tempting enough to expect a Fey or Dark warlock occasionally picking one. And the at-will should become an instant classic among charismatic human warlocks.

To round off the package, we are also given two flavorful and very potent magic items for warlocks. The Rod of Avernus allows for mass sliding of cursed enemies when you use your Pact Boon, an effect that already has me salivating (and has earned a quick spot in some of my friends' wishlists). As for the Armor of Dark Majesty, it confers a huge defensive bonus against cursed enemies, which honestly looks overpowered to me. We'll have to see if it survives the compilation errata.

Speaking of errata, there is one major bug in the article's mechanics that, well bugs me. Using damage type - changing weapons, you could potentially turn the HP cost of rerolling the new powers into resistable damage, most notably fire damage for tieflings with fire weapons, allowing you to essentially ignore the drawback. This really should be addressed. Apart from that, the article is quite a good read and very useful in play, so I can't help but recommend it.

Tuesday, April 6, 2010

One of the coolest ideas from the first Martial Power was Brash Assault, a Warlord at-will attack that leaves you open to an enemy counterattack which, in turn, allows an ally to hit the target. Unfortunately, the implementation leaves a bit to be desired, so this awesome power will, more often than not, be reduced to a mere melee basic attack. Here is a typical usage scenario:

Warlord: I move to flank the goblin with the fighter, and attack recklessly! Brash Assault!

DM: Ok, you hit.

Warlord: Great! I deal 7 points of damage, and he can make a free attack, but...

DM: He passes.

Warlord: Uh, what?

DM: The goblin doesn't make the attack. He knows your pal will hit back, and it's probably not worth it.

Warlord: (cry)

What really frustrates me about this power, is that it leaves completely up to the DM whether or not it works. Even worse, there is absolutely no drawback for the monster who chooses to do nothing. So, really, you have a Warlord asking his DM to please, please, please let him do cool things. Of course, the Warlord's ally will more often than not hit harder than the target, and chosing to attack tends to be a losing proposition for the monster. Unless there is a defender mark involve - then it becomes a massacre. From a strategic point of view, the 'right' choice for the DM will be, almost always, to do nothing. And, in the rare event where the monster's attack clearly outperforms that of the PCs, and there is no immediate risk of it getting killed... well, then the warlord might see the trigger work, but he would have been better off with a basic attack!

To complicate things further, we have the Role-Playing argument: "But the zombie/ooze/random-stupid-monster should ALWAYS choose to attack!". This enters the gray area of monster intelligence and tactics - generally, non-intelligent monsters will have less sophisticated tactics than intelligent ones. There are guidelines about monsters too stupid to look for flanks and the like, but no official rulings whatsoever. So it's up to each DM whether to exaggerate personality traits of certain monsters through their tactics, or to play at the best of his strategic abilities, occasionally giving up complex plays where it would be inappropiate for a monster. One thing is for sure, though - a target of Brash Assault knows how the effect works.

What would this mean for the stupid monster scenario? Even if it doesn't fully understand what's going on, the monster should know that it will get hurt if it counterattacks. If it hasn't seen the warlord's ally in action yet, it may not know just how much of a beating it will take - in this case, it may be legitimate to bite the bullet and attack. If the adjacent barbarian with a greataxe has just hit it for a gazillion damage, though... well, I could see even a zombie hesitating in that case. And I don't think the 'stupid monster' clause should never, ever serve as an excuse to make a Brash Assault counterattack through a defender's mark - that's downright suicidal, and anything smart enough to make an opportunity attack should know better.

The conclusion, then, is that it is very hard to justify choosing Brash Assault as a power, and using it in battle. We could leave it at that, but I really love the concept, so I'd like to rewrite the power so that it works. This is what this blog is about, after all.

Making it work without appealing to DM charity

There are several points that a fixed version of Brash Assault should address:

The effect should present the DM a legitimate choice. This means that refusing to take the attack should have a significant drawback.

Alternatively, we might force the enemy to make the counterattack.

It is not desirable to allow Warlords with polearms to abuse the fact that an enemy without reach is unable to counterattack.

Similarly, abuses with defender marks should be prevented.

As a final consideration, I think there should be a feeling of risk, of gambling, when using this power. This should have a relatively small chance of being downright great, but also of backfiring in some way. Also, some nod to the bravura warlord would be appropriate, since the build is clearly related to this power.

This is my take on the power:

Brash Assault

Miss: The marked condition ends on the target. You provoke an opportunity attack from the target, and the target must make the attack if able. If the opportunity attack hits or misses you, an ally of your choice within 5 squares of the target can make a basic attack against the target as a free action.

(Edited: removed combat advantage in the free attack to adjust power level)

So, how does this one work? Basically, it's a normal attack if you hit, and an exchange of blows if you miss. It shouldn't be difficult to set it up so that your ally's attack is stronger than the target's, at which point, the trade is in your favour - and missing becomes a good thing. Nevertheless, barring very strange scenarios, I doubt you'll ever get to the point where you'd rather miss than hit. The mark-removing clause requires a bit of extra coordination with your defender, but is necessary to prevent easy exploits. Likewise, the requirement that the enemy attack 'hits or misses' forces polearm users to play fair and take the blow. It also prevents the power from working against blinded, dazed or stunned opponents, so watch out.

Overall, I think this version is a reasonable power that you can play without feeling embarrased or causing trouble at your table. That said, the number and quality of at-will powers that Warlords have at their disposal after Martial Power 2 is remarkable, and the competition for the slot should be fierce!

If you are interested in the subject, there is an in-depth discussion about the power at the official errata forums, from a year ago.